What Version of Windows do I have? 32-Bit or 64-Bit?

Many new computers are shipping with 64-bit version of Windows 7. There was also a 64-bit version of Vista. There was even a very limited release of Windows XP that was 64-bit but if you have that you will know. So, if you came here for an answer to this question and you have Windows XP, there is a 99.99% chance that you are running 32-bit.
For those of you with Windows Vista or Windows 7, see the short guide below to help you figure this out: